Question

if a transversal intersect two parallel lines such that the ratio between interior angles is 2:7 then what is the measure of the greater angle​

Answer 1

Answer:

answer is 140°....................

Answer 2

Given :-

A transversal intersect two parallel lines such that the ratio between interior angles is 2:7.

To Find :-

The measure of the greater angle​.

Analysis :-

Consider the common ratio as an variable. Then the sides would be '2x' and '7x'

According to the question, make an equation and get the value of the variable.

Substitute the value of variable in the angles.

Solution :-

According to the question,

If a transversal intersect two parallel lines at each other, the interior angle would be supplementary i.e. total degree would be 180°

Let the common ratio be 'x'. Then the angles would be '2x' and '7x'

Making an equation,

$\sf 2x+7x=180$

$\sf 9x=180$

Finding the value of x,

$\sf x=\dfrac{180}{9}$

$\sf x=20^{o}$

Greatest angle = 7x

= 7 × 20 = 140°

Therefore, the measure of the greater angle is 140°